// Copyright 2015 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
//
// IntervalSet<T> is a data structure used to represent a sorted set of
// non-empty, non-adjacent, and mutually disjoint intervals. Mutations to an
// interval set preserve these properties, altering the set as needed. For
// example, adding [2, 3) to a set containing only [1, 2) would result in the
// set containing the single interval [1, 3).
//
// Supported operations include testing whether an Interval is contained in the
// IntervalSet, comparing two IntervalSets, and performing IntervalSet union,
// intersection, and difference.
//
// IntervalSet maintains the minimum number of entries needed to represent the
// set of underlying intervals. When the IntervalSet is modified (e.g. due to an
// Add operation), other interval entries may be coalesced, removed, or
// otherwise modified in order to maintain this invariant. The intervals are
// maintained in sorted order, by ascending min() value.
//
// The reader is cautioned to beware of the terminology used here: this library
// uses the terms "min" and "max" rather than "begin" and "end" as is
// conventional for the STL. The terminology [min, max) refers to the half-open
// interval which (if the interval is not empty) contains min but does not
// contain max. An interval is considered empty if min >= max.
//
// T is required to be default- and copy-constructible, to have an assignment
// operator, a difference operator (operator-()), and the full complement of
// comparison operators (<, <=, ==, !=, >=, >). These requirements are inherited
// from Interval<T>.
//
// IntervalSet has constant-time move operations.
//
// This class is thread-compatible if T is thread-compatible. (See
// go/thread-compatible).
//
// Examples:
//   IntervalSet<int> intervals;
//   intervals.Add(Interval<int>(10, 20));
//   intervals.Add(Interval<int>(30, 40));
//   // intervals contains [10,20) and [30,40).
//   intervals.Add(Interval<int>(15, 35));
//   // intervals has been coalesced. It now contains the single range [10,40).
//   EXPECT_EQ(1, intervals.Size());
//   EXPECT_TRUE(intervals.Contains(Interval<int>(10, 40)));
//
//   intervals.Difference(Interval<int>(10, 20));
//   // intervals should now contain the single range [20, 40).
//   EXPECT_EQ(1, intervals.Size());
//   EXPECT_TRUE(intervals.Contains(Interval<int>(20, 40)));

#ifndef NET_QUIC_INTERVAL_SET_H_
#define NET_QUIC_INTERVAL_SET_H_

#include <stddef.h>

#include <algorithm>
#include <set>
#include <string>
#include <utility>
#include <vector>

#include "base/logging.h"
#include "net/quic/interval.h"

namespace net {

template <typename T>
class IntervalSet {
private:
    struct IntervalComparator {
        bool operator()(const Interval<T>& a, const Interval<T>& b) const;
    };
    typedef std::set<Interval<T>, IntervalComparator> Set;

public:
    typedef typename Set::value_type value_type;
    typedef typename Set::const_iterator const_iterator;
    typedef typename Set::const_reverse_iterator const_reverse_iterator;

    // Instantiates an empty IntervalSet.
    IntervalSet() { }

    // Instantiates an IntervalSet containing exactly one initial half-open
    // interval [min, max), unless the given interval is empty, in which case the
    // IntervalSet will be empty.
    explicit IntervalSet(const Interval<T>& interval) { Add(interval); }

    // Instantiates an IntervalSet containing the half-open interval [min, max).
    IntervalSet(const T& min, const T& max) { Add(min, max); }

// TODO(rtenneti): Implement after suupport for std::initializer_list.
#if 0
  IntervalSet(std::initializer_list<value_type> il) { assign(il); }
#endif

    // Clears this IntervalSet.
    void Clear() { intervals_.clear(); }

    // Returns the number of disjoint intervals contained in this IntervalSet.
    size_t Size() const { return intervals_.size(); }

    // Returns the smallest interval that contains all intervals in this
    // IntervalSet, or the empty interval if the set is empty.
    Interval<T> SpanningInterval() const;

    // Adds "interval" to this IntervalSet. Adding the empty interval has no
    // effect.
    void Add(const Interval<T>& interval);

    // Adds the interval [min, max) to this IntervalSet. Adding the empty interval
    // has no effect.
    void Add(const T& min, const T& max) { Add(Interval<T>(min, max)); }

    // DEPRECATED(kosak). Use Union() instead. This method merges all of the
    // values contained in "other" into this IntervalSet.
    void Add(const IntervalSet& other);

    // Returns true if this IntervalSet represents exactly the same set of
    // intervals as the ones represented by "other".
    bool Equals(const IntervalSet& other) const;

    // Returns true if this IntervalSet is empty.
    bool Empty() const { return intervals_.empty(); }

    // Returns true if any interval in this IntervalSet contains the indicated
    // value.
    bool Contains(const T& value) const;

    // Returns true if there is some interval in this IntervalSet that wholly
    // contains the given interval. An interval O "wholly contains" a non-empty
    // interval I if O.Contains(p) is true for every p in I. This is the same
    // definition used by Interval<T>::Contains(). This method returns false on
    // the empty interval, due to a (perhaps unintuitive) convention inherited
    // from Interval<T>.
    // Example:
    //   Assume an IntervalSet containing the entries { [10,20), [30,40) }.
    //   Contains(Interval(15, 16)) returns true, because [10,20) contains
    //   [15,16). However, Contains(Interval(15, 35)) returns false.
    bool Contains(const Interval<T>& interval) const;

    // Returns true if for each interval in "other", there is some (possibly
    // different) interval in this IntervalSet which wholly contains it. See
    // Contains(const Interval<T>& interval) for the meaning of "wholly contains".
    // Perhaps unintuitively, this method returns false if "other" is the empty
    // set. The algorithmic complexity of this method is O(other.Size() *
    // log(this->Size())), which is not efficient. The method could be rewritten
    // to run in O(other.Size() + this->Size()).
    bool Contains(const IntervalSet<T>& other) const;

    // Returns true if there is some interval in this IntervalSet that wholly
    // contains the interval [min, max). See Contains(const Interval<T>&).
    bool Contains(const T& min, const T& max) const
    {
        return Contains(Interval<T>(min, max));
    }

    // Returns true if for some interval in "other", there is some interval in
    // this IntervalSet that intersects with it. See Interval<T>::Intersects()
    // for the definition of interval intersection.
    bool Intersects(const IntervalSet& other) const;

    // Returns an iterator to the Interval<T> in the IntervalSet that contains the
    // given value. In other words, returns an iterator to the unique interval
    // [min, max) in the IntervalSet that has the property min <= value < max. If
    // there is no such interval, this method returns end().
    const_iterator Find(const T& value) const;

    // Returns an iterator to the Interval<T> in the IntervalSet that wholly
    // contains the given interval. In other words, returns an iterator to the
    // unique interval outer in the IntervalSet that has the property that
    // outer.Contains(interval). If there is no such interval, or if interval is
    // empty, returns end().
    const_iterator Find(const Interval<T>& interval) const;

    // Returns an iterator to the Interval<T> in the IntervalSet that wholly
    // contains [min, max). In other words, returns an iterator to the unique
    // interval outer in the IntervalSet that has the property that
    // outer.Contains(Interval<T>(min, max)). If there is no such interval, or if
    // interval is empty, returns end().
    const_iterator Find(const T& min, const T& max) const
    {
        return Find(Interval<T>(min, max));
    }

    // Returns true if every value within the passed interval is not Contained
    // within the IntervalSet.
    bool IsDisjoint(const Interval<T>& interval) const;

    // Merges all the values contained in "other" into this IntervalSet.
    void Union(const IntervalSet& other);

    // Modifies this IntervalSet so that it contains only those values that are
    // currently present both in *this and in the IntervalSet "other".
    void Intersection(const IntervalSet& other);

    // Mutates this IntervalSet so that it contains only those values that are
    // currently in *this but not in "interval".
    void Difference(const Interval<T>& interval);

    // Mutates this IntervalSet so that it contains only those values that are
    // currently in *this but not in the interval [min, max).
    void Difference(const T& min, const T& max);

    // Mutates this IntervalSet so that it contains only those values that are
    // currently in *this but not in the IntervalSet "other".
    void Difference(const IntervalSet& other);

    // Mutates this IntervalSet so that it contains only those values that are
    // in [min, max) but not currently in *this.
    void Complement(const T& min, const T& max);

    // IntervalSet's begin() iterator. The invariants of IntervalSet guarantee
    // that for each entry e in the set, e.min() < e.max() (because the entries
    // are non-empty) and for each entry f that appears later in the set,
    // e.max() < f.min() (because the entries are ordered, pairwise-disjoint, and
    // non-adjacent). Modifications to this IntervalSet invalidate these
    // iterators.
    const_iterator begin() const { return intervals_.begin(); }

    // IntervalSet's end() iterator.
    const_iterator end() const { return intervals_.end(); }

    // IntervalSet's rbegin() and rend() iterators. Iterator invalidation
    // semantics are the same as those for begin() / end().
    const_reverse_iterator rbegin() const { return intervals_.rbegin(); }

    const_reverse_iterator rend() const { return intervals_.rend(); }

    // Appends the intervals in this IntervalSet to the end of *out.
    void Get(std::vector<Interval<T>>* out) const
    {
        out->insert(out->end(), begin(), end());
    }

    // Copies the intervals in this IntervalSet to the given output iterator.
    template <typename Iter>
    Iter Get(Iter out_iter) const
    {
        return std::copy(begin(), end(), out_iter);
    }

    template <typename Iter>
    void assign(Iter first, Iter last)
    {
        Clear();
        for (; first != last; ++first)
            Add(*first);
    }

// TODO(rtenneti): Implement after suupport for std::initializer_list.
#if 0
  void assign(std::initializer_list<value_type> il) {
    assign(il.begin(), il.end());
  }
#endif

    // Returns a human-readable representation of this set. This will typically be
    // (though is not guaranteed to be) of the form
    //   "[a1, b1) [a2, b2) ... [an, bn)"
    // where the intervals are in the same order as given by traversal from
    // begin() to end(). This representation is intended for human consumption;
    // computer programs should not rely on the output being in exactly this form.
    std::string ToString() const;

    // Equality for IntervalSet<T>. Delegates to Equals().
    bool operator==(const IntervalSet& other) const { return Equals(other); }

    // Inequality for IntervalSet<T>. Delegates to Equals() (and returns its
    // negation).
    bool operator!=(const IntervalSet& other) const { return !Equals(other); }

// TODO(rtenneti): Implement after suupport for std::initializer_list.
#if 0
  IntervalSet& operator=(std::initializer_list<value_type> il) {
    assign(il.begin(), il.end());
    return *this;
  }
#endif

    // Swap this IntervalSet with *other. This is a constant-time operation.
    void Swap(IntervalSet<T>* other) { intervals_.swap(other->intervals_); }

private:
    // Removes overlapping ranges and coalesces adjacent intervals as needed.
    void Compact(const typename Set::iterator& begin,
        const typename Set::iterator& end);

    // Returns true if this set is valid (i.e. all intervals in it are non-empty,
    // non-adjacent, and mutually disjoint). Currently this is used as an
    // integrity check by the Intersection() and Difference() methods, but is only
    // invoked for debug builds (via DCHECK).
    bool Valid() const;

    // Finds the first interval that potentially intersects 'other'.
    const_iterator FindIntersectionCandidate(const IntervalSet& other) const;

    // Finds the first interval that potentially intersects 'interval'.
    const_iterator FindIntersectionCandidate(const Interval<T>& interval) const;

    // Helper for Intersection() and Difference(): Finds the next pair of
    // intervals from 'x' and 'y' that intersect. 'mine' is an iterator
    // over x->intervals_. 'theirs' is an iterator over y.intervals_. 'mine'
    // and 'theirs' are advanced until an intersecting pair is found.
    // Non-intersecting intervals (aka "holes") from x->intervals_ can be
    // optionally erased by "on_hole".
    template <typename X, typename Func>
    static bool FindNextIntersectingPairImpl(X* x,
        const IntervalSet& y,
        const_iterator* mine,
        const_iterator* theirs,
        Func on_hole);

    // The variant of the above method that doesn't mutate this IntervalSet.
    bool FindNextIntersectingPair(const IntervalSet& other,
        const_iterator* mine,
        const_iterator* theirs) const
    {
        return FindNextIntersectingPairImpl(
            this, other, mine, theirs,
            [](const IntervalSet*, const_iterator, const_iterator) {});
    }

    // The variant of the above method that mutates this IntervalSet by erasing
    // holes.
    bool FindNextIntersectingPairAndEraseHoles(const IntervalSet& other,
        const_iterator* mine,
        const_iterator* theirs)
    {
        return FindNextIntersectingPairImpl(
            this, other, mine, theirs,
            [](IntervalSet* x, const_iterator from, const_iterator to) {
                x->intervals_.erase(from, to);
            });
    }

    // The representation for the intervals. The intervals in this set are
    // non-empty, pairwise-disjoint, non-adjacent and ordered in ascending order
    // by min().
    Set intervals_;
};

template <typename T>
std::ostream& operator<<(std::ostream& out, const IntervalSet<T>& seq);

template <typename T>
void swap(IntervalSet<T>& x, IntervalSet<T>& y);

//==============================================================================
// Implementation details: Clients can stop reading here.

template <typename T>
Interval<T> IntervalSet<T>::SpanningInterval() const
{
    Interval<T> result;
    if (!intervals_.empty()) {
        result.SetMin(intervals_.begin()->min());
        result.SetMax(intervals_.rbegin()->max());
    }
    return result;
}

template <typename T>
void IntervalSet<T>::Add(const Interval<T>& interval)
{
    if (interval.Empty())
        return;
    std::pair<typename Set::iterator, bool> ins = intervals_.insert(interval);
    if (!ins.second) {
        // This interval already exists.
        return;
    }
    // Determine the minimal range that will have to be compacted.  We know that
    // the IntervalSet was valid before the addition of the interval, so only
    // need to start with the interval itself (although Compact takes an open
    // range so begin needs to be the interval to the left).  We don't know how
    // many ranges this interval may cover, so we need to find the appropriate
    // interval to end with on the right.
    typename Set::iterator begin = ins.first;
    if (begin != intervals_.begin())
        --begin;
    const Interval<T> target_end(interval.max(), interval.max());
    const typename Set::iterator end = intervals_.upper_bound(target_end);
    Compact(begin, end);
}

template <typename T>
void IntervalSet<T>::Add(const IntervalSet& other)
{
    for (const_iterator it = other.begin(); it != other.end(); ++it) {
        Add(*it);
    }
}

template <typename T>
bool IntervalSet<T>::Equals(const IntervalSet& other) const
{
    if (intervals_.size() != other.intervals_.size())
        return false;
    for (typename Set::iterator i = intervals_.begin(),
                                j = other.intervals_.begin();
         i != intervals_.end(); ++i, ++j) {
        // Simple member-wise equality, since all intervals are non-empty.
        if (i->min() != j->min() || i->max() != j->max())
            return false;
    }
    return true;
}

template <typename T>
bool IntervalSet<T>::Contains(const T& value) const
{
    Interval<T> tmp(value, value);
    // Find the first interval with min() > value, then move back one step
    const_iterator it = intervals_.upper_bound(tmp);
    if (it == intervals_.begin())
        return false;
    --it;
    return it->Contains(value);
}

template <typename T>
bool IntervalSet<T>::Contains(const Interval<T>& interval) const
{
    // Find the first interval with min() > value, then move back one step.
    const_iterator it = intervals_.upper_bound(interval);
    if (it == intervals_.begin())
        return false;
    --it;
    return it->Contains(interval);
}

template <typename T>
bool IntervalSet<T>::Contains(const IntervalSet<T>& other) const
{
    if (!SpanningInterval().Contains(other.SpanningInterval())) {
        return false;
    }

    for (const_iterator i = other.begin(); i != other.end(); ++i) {
        // If we don't contain the interval, can return false now.
        if (!Contains(*i)) {
            return false;
        }
    }
    return true;
}

// This method finds the interval that Contains() "value", if such an interval
// exists in the IntervalSet. The way this is done is to locate the "candidate
// interval", the only interval that could *possibly* contain value, and test it
// using Contains(). The candidate interval is the interval with the largest
// min() having min() <= value.
//
// Determining the candidate interval takes a couple of steps. First, since the
// underlying std::set stores intervals, not values, we need to create a "probe
// interval" suitable for use as a search key. The probe interval used is
// [value, value). Now we can restate the problem as finding the largest
// interval in the IntervalSet that is <= the probe interval.
//
// This restatement only works if the set's comparator behaves in a certain way.
// In particular it needs to order first by ascending min(), and then by
// descending max(). The comparator used by this library is defined in exactly
// this way. To see why descending max() is required, consider the following
// example. Assume an IntervalSet containing these intervals:
//
//   [0, 5)  [10, 20)  [50, 60)
//
// Consider searching for the value 15. The probe interval [15, 15) is created,
// and [10, 20) is identified as the largest interval in the set <= the probe
// interval. This is the correct interval needed for the Contains() test, which
// will then return true.
//
// Now consider searching for the value 30. The probe interval [30, 30) is
// created, and again [10, 20] is identified as the largest interval <= the
// probe interval. This is again the correct interval needed for the Contains()
// test, which in this case returns false.
//
// Finally, consider searching for the value 10. The probe interval [10, 10) is
// created. Here the ordering relationship between [10, 10) and [10, 20) becomes
// vitally important. If [10, 10) were to come before [10, 20), then [0, 5)
// would be the largest interval <= the probe, leading to the wrong choice of
// interval for the Contains() test. Therefore [10, 10) needs to come after
// [10, 20). The simplest way to make this work in the general case is to order
// by ascending min() but descending max(). In this ordering, the empty interval
// is larger than any non-empty interval with the same min(). The comparator
// used by this library is careful to induce this ordering.
//
// Another detail involves the choice of which std::set method to use to try to
// find the candidate interval. The most appropriate entry point is
// set::upper_bound(), which finds the smallest interval which is > the probe
// interval. The semantics of upper_bound() are slightly different from what we
// want (namely, to find the largest interval which is <= the probe interval)
// but they are close enough; the interval found by upper_bound() will always be
// one step past the interval we are looking for (if it exists) or at begin()
// (if it does not). Getting to the proper interval is a simple matter of
// decrementing the iterator.
template <typename T>
typename IntervalSet<T>::const_iterator IntervalSet<T>::Find(
    const T& value) const
{
    Interval<T> tmp(value, value);
    const_iterator it = intervals_.upper_bound(tmp);
    if (it == intervals_.begin())
        return intervals_.end();
    --it;
    if (it->Contains(value))
        return it;
    else
        return intervals_.end();
}

// This method finds the interval that Contains() the interval "probe", if such
// an interval exists in the IntervalSet. The way this is done is to locate the
// "candidate interval", the only interval that could *possibly* contain
// "probe", and test it using Contains(). The candidate interval is the largest
// interval that is <= the probe interval.
//
// The search for the candidate interval only works if the comparator used
// behaves in a certain way. In particular it needs to order first by ascending
// min(), and then by descending max(). The comparator used by this library is
// defined in exactly this way. To see why descending max() is required,
// consider the following example. Assume an IntervalSet containing these
// intervals:
//
//   [0, 5)  [10, 20)  [50, 60)
//
// Consider searching for the probe [15, 17). [10, 20) is the largest interval
// in the set which is <= the probe interval. This is the correct interval
// needed for the Contains() test, which will then return true, because [10, 20)
// contains [15, 17).
//
// Now consider searching for the probe [30, 32). Again [10, 20] is the largest
// interval <= the probe interval. This is again the correct interval needed for
// the Contains() test, which in this case returns false, because [10, 20) does
// not contain [30, 32).
//
// Finally, consider searching for the probe [10, 12). Here the ordering
// relationship between [10, 12) and [10, 20) becomes vitally important. If
// [10, 12) were to come before [10, 20), then [0, 5) would be the largest
// interval <= the probe, leading to the wrong choice of interval for the
// Contains() test. Therefore [10, 12) needs to come after [10, 20). The
// simplest way to make this work in the general case is to order by ascending
// min() but descending max(). In this ordering, given two intervals with the
// same min(), the wider one goes before the narrower one. The comparator used
// by this library is careful to induce this ordering.
//
// Another detail involves the choice of which std::set method to use to try to
// find the candidate interval. The most appropriate entry point is
// set::upper_bound(), which finds the smallest interval which is > the probe
// interval. The semantics of upper_bound() are slightly different from what we
// want (namely, to find the largest interval which is <= the probe interval)
// but they are close enough; the interval found by upper_bound() will always be
// one step past the interval we are looking for (if it exists) or at begin()
// (if it does not). Getting to the proper interval is a simple matter of
// decrementing the iterator.
template <typename T>
typename IntervalSet<T>::const_iterator IntervalSet<T>::Find(
    const Interval<T>& probe) const
{
    const_iterator it = intervals_.upper_bound(probe);
    if (it == intervals_.begin())
        return intervals_.end();
    --it;
    if (it->Contains(probe))
        return it;
    else
        return intervals_.end();
}

template <typename T>
bool IntervalSet<T>::IsDisjoint(const Interval<T>& interval) const
{
    Interval<T> tmp(interval.min(), interval.min());
    // Find the first interval with min() > interval.min()
    const_iterator it = intervals_.upper_bound(tmp);
    if (it != intervals_.end() && interval.max() > it->min())
        return false;
    if (it == intervals_.begin())
        return true;
    --it;
    return it->max() <= interval.min();
}

template <typename T>
void IntervalSet<T>::Union(const IntervalSet& other)
{
    intervals_.insert(other.begin(), other.end());
    Compact(intervals_.begin(), intervals_.end());
}

template <typename T>
typename IntervalSet<T>::const_iterator
IntervalSet<T>::FindIntersectionCandidate(const IntervalSet& other) const
{
    return FindIntersectionCandidate(*other.intervals_.begin());
}

template <typename T>
typename IntervalSet<T>::const_iterator
IntervalSet<T>::FindIntersectionCandidate(const Interval<T>& interval) const
{
    // Use upper_bound to efficiently find the first interval in intervals_
    // where min() is greater than interval.min().  If the result
    // isn't the beginning of intervals_ then move backwards one interval since
    // the interval before it is the first candidate where max() may be
    // greater than interval.min().
    // In other words, no interval before that can possibly intersect with any
    // of other.intervals_.
    const_iterator mine = intervals_.upper_bound(interval);
    if (mine != intervals_.begin()) {
        --mine;
    }
    return mine;
}

template <typename T>
template <typename X, typename Func>
bool IntervalSet<T>::FindNextIntersectingPairImpl(X* x,
    const IntervalSet& y,
    const_iterator* mine,
    const_iterator* theirs,
    Func on_hole)
{
    CHECK(x != nullptr);
    if ((*mine == x->intervals_.end()) || (*theirs == y.intervals_.end())) {
        return false;
    }
    while (!(**mine).Intersects(**theirs)) {
        const_iterator erase_first = *mine;
        // Skip over intervals in 'mine' that don't reach 'theirs'.
        while (*mine != x->intervals_.end() && (**mine).max() <= (**theirs).min()) {
            ++(*mine);
        }
        on_hole(x, erase_first, *mine);
        // We're done if the end of intervals_ is reached.
        if (*mine == x->intervals_.end()) {
            return false;
        }
        // Skip over intervals 'theirs' that don't reach 'mine'.
        while (*theirs != y.intervals_.end() && (**theirs).max() <= (**mine).min()) {
            ++(*theirs);
        }
        // If the end of other.intervals_ is reached, we're done.
        if (*theirs == y.intervals_.end()) {
            on_hole(x, *mine, x->intervals_.end());
            return false;
        }
    }
    return true;
}

template <typename T>
void IntervalSet<T>::Intersection(const IntervalSet& other)
{
    if (!SpanningInterval().Intersects(other.SpanningInterval())) {
        intervals_.clear();
        return;
    }

    const_iterator mine = FindIntersectionCandidate(other);
    // Remove any intervals that cannot possibly intersect with other.intervals_.
    intervals_.erase(intervals_.begin(), mine);
    const_iterator theirs = other.FindIntersectionCandidate(*this);

    while (FindNextIntersectingPairAndEraseHoles(other, &mine, &theirs)) {
        // OK, *mine and *theirs intersect.  Now, we find the largest
        // span of intervals in other (starting at theirs) - say [a..b]
        // - that intersect *mine, and we replace *mine with (*mine
        // intersect x) for all x in [a..b] Note that subsequent
        // intervals in this can't intersect any intervals in [a..b) --
        // they may only intersect b or subsequent intervals in other.
        Interval<T> i(*mine);
        intervals_.erase(mine);
        mine = intervals_.end();
        Interval<T> intersection;
        while (theirs != other.intervals_.end() && i.Intersects(*theirs, &intersection)) {
            std::pair<typename Set::iterator, bool> ins = intervals_.insert(intersection);
            DCHECK(ins.second);
            mine = ins.first;
            ++theirs;
        }
        DCHECK(mine != intervals_.end());
        --theirs;
        ++mine;
    }
    DCHECK(Valid());
}

template <typename T>
bool IntervalSet<T>::Intersects(const IntervalSet& other) const
{
    if (!SpanningInterval().Intersects(other.SpanningInterval())) {
        return false;
    }

    const_iterator mine = FindIntersectionCandidate(other);
    if (mine == intervals_.end()) {
        return false;
    }
    const_iterator theirs = other.FindIntersectionCandidate(*mine);

    return FindNextIntersectingPair(other, &mine, &theirs);
}

template <typename T>
void IntervalSet<T>::Difference(const Interval<T>& interval)
{
    if (!SpanningInterval().Intersects(interval)) {
        return;
    }
    Difference(IntervalSet<T>(interval));
}

template <typename T>
void IntervalSet<T>::Difference(const T& min, const T& max)
{
    Difference(Interval<T>(min, max));
}

template <typename T>
void IntervalSet<T>::Difference(const IntervalSet& other)
{
    if (!SpanningInterval().Intersects(other.SpanningInterval())) {
        return;
    }

    const_iterator mine = FindIntersectionCandidate(other);
    // If no interval in mine reaches the first interval of theirs then we're
    // done.
    if (mine == intervals_.end()) {
        return;
    }
    const_iterator theirs = other.FindIntersectionCandidate(*this);

    while (FindNextIntersectingPair(other, &mine, &theirs)) {
        // At this point *mine and *theirs overlap.  Remove mine from
        // intervals_ and replace it with the possibly two intervals that are
        // the difference between mine and theirs.
        Interval<T> i(*mine);
        intervals_.erase(mine++);
        Interval<T> lo;
        Interval<T> hi;
        i.Difference(*theirs, &lo, &hi);

        if (!lo.Empty()) {
            // We have a low end.  This can't intersect anything else.
            std::pair<typename Set::iterator, bool> ins = intervals_.insert(lo);
            DCHECK(ins.second);
        }

        if (!hi.Empty()) {
            std::pair<typename Set::iterator, bool> ins = intervals_.insert(hi);
            DCHECK(ins.second);
            mine = ins.first;
        }
    }
    DCHECK(Valid());
}

template <typename T>
void IntervalSet<T>::Complement(const T& min, const T& max)
{
    IntervalSet<T> span(min, max);
    span.Difference(*this);
    intervals_.swap(span.intervals_);
}

template <typename T>
std::string IntervalSet<T>::ToString() const
{
    std::ostringstream os;
    os << *this;
    return os.str();
}

// This method compacts the IntervalSet, merging pairs of overlapping intervals
// into a single interval. In the steady state, the IntervalSet does not contain
// any such pairs. However, the way the Union() and Add() methods work is to
// temporarily put the IntervalSet into such a state and then to call Compact()
// to "fix it up" so that it is no longer in that state.
//
// Compact() needs the interval set to allow two intervals [a,b) and [a,c)
// (having the same min() but different max()) to briefly coexist in the set at
// the same time, and be adjacent to each other, so that they can be efficiently
// located and merged into a single interval. This state would be impossible
// with a comparator which only looked at min(), as such a comparator would
// consider such pairs equal. Fortunately, the comparator used by IntervalSet
// does exactly what is needed, ordering first by ascending min(), then by
// descending max().
template <typename T>
void IntervalSet<T>::Compact(const typename Set::iterator& begin,
    const typename Set::iterator& end)
{
    if (begin == end)
        return;
    typename Set::iterator next = begin;
    typename Set::iterator prev = begin;
    typename Set::iterator it = begin;
    ++it;
    ++next;
    while (it != end) {
        ++next;
        if (prev->max() >= it->min()) {
            // Overlapping / coalesced range; merge the two intervals.
            T min = prev->min();
            T max = std::max(prev->max(), it->max());
            Interval<T> i(min, max);
            intervals_.erase(prev);
            intervals_.erase(it);
            std::pair<typename Set::iterator, bool> ins = intervals_.insert(i);
            DCHECK(ins.second);
            prev = ins.first;
        } else {
            prev = it;
        }
        it = next;
    }
}

template <typename T>
bool IntervalSet<T>::Valid() const
{
    const_iterator prev = end();
    for (const_iterator it = begin(); it != end(); ++it) {
        // invalid or empty interval.
        if (it->min() >= it->max())
            return false;
        // Not sorted, not disjoint, or adjacent.
        if (prev != end() && prev->max() >= it->min())
            return false;
        prev = it;
    }
    return true;
}

template <typename T>
inline std::ostream& operator<<(std::ostream& out, const IntervalSet<T>& seq)
{
// TODO(rtenneti): Implement << method of IntervalSet.
#if 0
  util::gtl::LogRangeToStream(out, seq.begin(), seq.end(),
                              util::gtl::LogLegacy());
#endif // 0
    return out;
}

template <typename T>
void swap(IntervalSet<T>& x, IntervalSet<T>& y)
{
    x.Swap(&y);
}

// This comparator orders intervals first by ascending min() and then by
// descending max(). Readers who are satisified with that explanation can stop
// reading here. The remainder of this comment is for the benefit of future
// maintainers of this library.
//
// The reason for this ordering is that this comparator has to serve two
// masters. First, it has to maintain the intervals in its internal set in the
// order that clients expect to see them. Clients see these intervals via the
// iterators provided by begin()/end() or as a result of invoking Get(). For
// this reason, the comparator orders intervals by ascending min().
//
// If client iteration were the only consideration, then ordering by ascending
// min() would be good enough. This is because the intervals in the IntervalSet
// are non-empty, non-adjacent, and mutually disjoint; such intervals happen to
// always have disjoint min() values, so such a comparator would never even have
// to look at max() in order to work correctly for this class.
//
// However, in addition to ordering by ascending min(), this comparator also has
// a second responsibility: satisfying the special needs of this library's
// peculiar internal implementation. These needs require the comparator to order
// first by ascending min() and then by descending max(). The best way to
// understand why this is so is to check out the comments associated with the
// Find() and Compact() methods.
template <typename T>
inline bool IntervalSet<T>::IntervalComparator::operator()(
    const Interval<T>& a,
    const Interval<T>& b) const
{
    return (a.min() < b.min() || (a.min() == b.min() && a.max() > b.max()));
}

} // namespace net

#endif // NET_QUIC_INTERVAL_SET_H_
